Assignment-1

# Assignment-1 - MECH646 Wheeled Mobile Robots Danielle Sami...

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MECH646 Wheeled Mobile Robots Danielle Sami Nasrallah Department of Mechanical Engineering Faculty of Engineering and Architecture American University of Beirut 2010-10-28

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ASSIGNMENT 1 Exercise 1: Falling rolling disk In this exercise we consider a falling rolling disk, which corresponds, of course, to a more realistic case than the example studied in class. Figure 1: Falling Rolling Disk 1. Define the vector q of generalized coordinates 2. Compute the angular velocity of the falling rolling disk 3. Compute the velocity of the centre of the disk under the pure-rolling assumption 4. Derive the kinematic constraints 5. Write the kinematic constraints in the Pfaﬃan form 6. Apply the Frobenius theorem to show the nonholonomy of the falling rolling disk
Exercise 2: Omnidirectional symmetric three-wheeled mobile robot The robot has three Omni-directional wheels located at three non-consecutive sides of a regular hexagon, as illustrated in Fig.2. Contrary to conventional wheels, where under pure-
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